Decomposing Berge Graphs Containing Proper Wheels

work in progress

l'vlichclc Conforti * Gerard Cornu6jols ·1

Kristina Vuskovic +

and G iacorno Zambelli §

April 2001, July 2001, l\larch 2002

Abstract

If a 13erge graph contains certain \vheels, then it contains a "good" skew partition.

1 Introduction

A graph G is perfect if, for all induced subgraphs of G, the size of a largest clique is equal to the chromatic number [1]. Lovasz [8] shmved that a graph G is perfect if and only if its complement G is perfect. A graph is minimally

*Dipartimento di l\Iatematica Pura ed Applicata, Universita di Padova , Via Belzoni 7, 35131 Padova, Italy. confortiC!'!irnath.unipd.it

·1·GSIA, Carnegie Mellon University, Schenley Park, Pittsburgh, PA 15213, USA. gc:Ov{~andrew.cmu.edu

+School of Computing, University of Leeds, Leedt-; LS2 9.JT, UK. vuskovi@comp.leeds.ac.uk

§GSIA, Carnegie .rviellon University, Schenley Park, Pittsburgh, PA 15213, USA. gia­comoC~'iiandrevv.crnu.edu

This work was supported in part by NSF grant D.l\U-9802773 and O~R grant N00014-97-1-0196.